On calculation of stress-strain state of steel closed ropes in extension and twisting. Part 1. Determination of generalized stiffness and deformation coefficients

Abstract

Comparative analysis of the results of determination of generalized coefficients of stiffness and deformation for closed hoisting rope in extension and twisting was conducted via analytical calculation, using generalized static equations and computer finite element modeling. Computer modeling allows to determine the resulting values of axial force P and torque M in closed rope via summarizing of the values of internal forces and torques in the layers that are laid with different directions. It decreases calculation w orkability for the rope stress-strain state. It is shown that the results of analytical calculation of generalized stiffness and deformation coefficients in rope twisting differ by 24 % in average with the results of finite element calculation, based on the static equations. The value of rope elasticity module Ек corresponds to the values of elasticity module for closed ropes during the first loading. Analytical calculation provides the values of Ек module exceeding by 6–7 % the average value of elasticity module of closed ropes (Ек = 160 GPа), that is achieved by preliminary elongation (elastic-plastic extension). It was established that analytical calculation of the stiffness coefficient in twisting does not provide the reliable results owing to absence of accounting the difference in directions of laying of rope layers. Coincidence or opposition in directions of laying of rope layers and torque determines respectively extension or compression of rope layer wires in twisting. Untwisting of the external layer, consisting of Z-shape wires, leads to unloading of the layer and gap forming between wires, while this gap exceeds the allowance on wire dimension and promotes violation of rope structural integrity.